Question

Hi I need to find the solution set for the following equation √(10x+5) - √(6x-11) =6

Answer 1

you sure that is a "-" and not a "+"?

Answer 2

Yes the equation is correct

Answer 3

too bad because if it was a +, 2 would work by inspection. this problem is a pain. you have to square twice

Answer 4

And it says solve the equation. The solution set is blank and blank

Answer 5

ok let me work it out. i was trying to guess what would give a perfect square for 10x+5 and 6x-11

Answer 6

Thx

Answer 7

2 works because 2*10+5=25 and 6*2-11=1

Answer 8

and 5+1=6

Answer 9

So would the sol set be 5,1

Answer 10

no the solution would be x = 2, but it is not. i am still working.

Answer 11

have to square both sides, then square again. i will show you but i want to get a correct answer so i don't blow it.

Answer 12

good heavens. i will be back in ten minutes with the answer and the algebra. hold on.

Answer 13

K :-)

Answer 14

62

Answer 15

is the answer

Answer 16

would you like a worked out solution?

Answer 17

square both sided.
you will get
\[16x-6-2\sqrt{(10x+5)(6x-11)}=36\]

Answer 18

\[-2\sqrt{(10x+5)(6x-11)}=42-16x\]

Answer 19

divide by -2
\[\sqrt{(10x+5)(6x-11)}=8x-21\]

Answer 20

so is there only one solution of 62

Answer 21

sorry my computer is slow

Answer 22

then square again. you will get
\[(10x-5)(6x-11)=(8x+21)^2\]

Answer 23

yes only one answer. you will solve a quadratic and get two solutions but only one will work.

Answer 24

introduced a false solution when you squared

Answer 25

typo on last answer. it should have been
\[(10x+5)(6x-11)=(8x-21)^2\]

Answer 26

thx u

Answer 27

expand these to get
\[60x^2-80x-55=64x^2-336x+441\]

Answer 28

set =0 and solve:
\[4x^2-256x+496=0\]
divide by 4
\[x^2-64x+124=0\]

Answer 29

factor
\[(x-62)(x-2)=0\]
\[x=62\] or \[x=2\]

Answer 30

but there is only one answer because 2 does not work. if you replace x by 2 in the original equation you get
\[\sqrt{25}-\sqrt{1}=6\]
\[5-1=6\]

which is false.

Answer 31

negatives on both?? thx

Answer 32

62 will work but only 62, not 2.

Answer 33

oh negatives on both when factoring. but the only answer is x = 62

Answer 34

you have to plug it into the original equation

Answer 35

\[\sqrt{10\times 62+5}-\sqrt{6\times 62-11}\]
\[\sqrt{625}-\sqrt{361}=25-19=6\]

Answer 36

i am confused i just need the solution set

Answer 37

solution is 62

Answer 38

62 works, 2 does not

Answer 39

ok...thx